Question

Prove 3+2roots5 is a irrational number

Answer 1

3+2√5=3+8=11
hope it helps

Answer 2

Let 3 + 2√5 be rational.

So,

3 + 2√5 = a / b ( a and b are co primes and b ≠ 0 )

2√5 = ( a - 3b ) / b             ( Take b as LCM )

√5 = ( a - 3b ) / 2b

Since a, b, 2 and 3 are integers

( a - 3b ) / 2b is rational.

But √5 is irrational.

Irrational ≠ Rational

Therefore, 3 + 2√5 is irrational.